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KVL in Ac circuits

  1. Nov 1, 2012 #1

    Why do we use KVL in Ac circuits ?! or to be more specific is it accurate to use it in Ac circuit , just the same accuracy as using it in Dc ?!

    Doesn't the current that pass through the circuit itself make it's own variable magnetic field , which crosses the loop of the circle , making ∫E.dl = -d∅/dt , so in the circuit loop we can't say that the field is conservative anymore ?!

    also we have the Ac source it self , which functions by rotating into the magnetic field or by applying a time changing magnetic field , so if we expand the circuit diagram and instead of putting the famous "shape" of a sinusoidal voltage source , we but the whole device , we will see also varying magnetic field of another magnitude passing through that part of the circuit

    I may think that the second thing I said is already taken into consideration , and that's why we put a voltage source "shape of a sinusoidal voltage source" I just try to get the whole picture .

    so , wether we have coils or not in the circuit , doesn't the time-varying current it self make a change to KVL ?!
  2. jcsd
  3. Nov 1, 2012 #2
    Unfortunately most textbooks rewrite KVL in a form equating to zero.

    If you use the original form of KVL

    The sum of the Emfs = The sum of the IR products

    Then all is well with KVL (poetry)

    If a magnetic field or other agent injects an EMF into the circuit then that EMF appears on the left hand side of the equation.

    If that injected EMF is time varying then KVL refers to the instantaneous circuit or to a time averaged set of voltages and currents.
    Last edited: Nov 1, 2012
  4. Nov 1, 2012 #3


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    You are right to ask the question as the situation is not as straightforward, as you have shown. However, as long as you are dealing with a circuit in which you can assume 'lumped components' then Kircholff's Second Law can be applied. This works for many many cases of circuit design, for instance when the value marked on the side of a components are what it says and at frequencies where the layout is not critical.
  5. Nov 1, 2012 #4
    thank you ,

    For some reason I may need to read more about this topic , can you tell me about a good source /book talking about it ?! or some lecture vedio ?

    furthermore , about what I said about the time varying current , we know that the (B) resulting from a current loop at the centre = u I / 2R ( providing it's circular) so the ∅ = ∏RuI/2 (( just assuming it is uniform for it will not affect too much)
    ) and emf = ∏Ru/2 *dI/dt
    and to get considerable voltage we need the amplitude of I be a very large number
    Does it happen in reality that the ∏*R*Imax equal a large number to make considerable emf ?! ( I don't know what amperes can be used , does any thing use kilo-amperes or mega-amperes in any circuit ?! ( I know ampere it self is a high value and of course that thing will not be a house-machine) .

    I just now saw this " conflict :) "


    that some how relieves me as I get to know ( as you told me) that there really is something worth thinking about , and I don't know why something like this is not popular on the internet or textbooks , even if it doesn't affect circuit analysis in a dangerous way.

    thanks again , and waiting for a source if there were one , and no problem for it to be more sophisticated or higher level as it doesn't have to be me who reads or watches it :)
  6. Nov 1, 2012 #5


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    Good point - why is it not taught? Well, if every slightly dodgy approximation were to be pointed out to students, lessons and lectures would end up as a list of parentheses that would never be resolved. Kirchoff works exceedingly well - just like Newton's Laws of Motion. You can usually rely (in your education) that you will not be 'tested' on situations where they run out of steam until you know enough to deal with it.

    Every piece of wire is an antenna! That would be a bad way to start your day at the Audio Amplifier Design Desk or the National Grid Control Room.
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